Cost-Volume-Profit: Robert Company operates a manufacturing facility in Paris. A
ID: 2497793 • Letter: C
Question
Cost-Volume-Profit:
Robert Company operates a manufacturing facility in Paris. Annual fixed costs for this facility are $820,000. The firm has two products, X and Y, which have selling prices of $80 and $50 per unit, respectively. Variable costs for units of X and Y are $30 and $10 per unit, respectively. The firm sells four times as many units of Y as units of X.
Required: Based on the information above, how many units of X have to be sold for the firm to break even in any given year?
_________ units of X
Explanation / Answer
For break even analysis, Selling Pric(SP)e should be equal to Cost Price(CP).
SP = CP
Taking this formula we will calculate the units to be sold in a year to break even.
It is mentioned in question that firm sells four times of units of Y as of X. So we suppose that if firm sells total of X units in a year therefore for Product Y it sells 4X. Based on it below table is drawn -
10
SP = Units of Product X* SP per unit + Units of Product Y*SP per Unit
Similarly CP = Units of ProductX* CP per unit+Units of Product Y * CP per unit + Fixed Cost
We suppose Units of Product X = x and Units of Product Y = 4x (four times of Product X)
On basis , SP = x*80 + 4x*50
Similarly, CP = VC + FC = x*30 + 4x*10 + 820,000 (Fixed Cost)
When SP = CP; 80x+4x*50 = 30x+4x*10+820,000
80x+200x = 30x + 40x + 820,000
280x = 70x + 820,000
280x - 70x = 820,000
210x = 820,000
x = 820,000/210 = 3904.76
Units of Product X to be sold in a year is 3904.76 or 3905 units
And units of Product Y to be sold in a year is 3904.76 * 4 = 15 619.04 or 15,619 units.
Workings :-
SP = Selling Price
CP = Cost Price
P = Profit
VC = Variable Cost
For Breakeven , SP = CP which is calculated as below -
SP = CP + Profit
If profit is zero then SP will be equal to CP. Based on this formula we calculate units to be sold in a year.
Product X Product Y X 4x SP per unit(in dollars) 80 50 VC per unit(in dollars) 3010